In my experience no one is really all that comfortable with their character until 2 or 3 sessions in. This can be more confined in systems like Pathfinder where build options are a bit limited once you start down a path, but for this post I'm talking about more point buy games like L5R rather than level based systems like D&D and pathfinder.
Now, I've noticed this trend strongly enough that I generally invite my players to talk to me and ask about tweaking things on their sheets over those first few sessions. Maybe an advantage doesn't fit the character with how he is played. Maybe a character needs a different hook in her backstory to make her work, and that hook requires different skills. The point is the first few sessions are where everyone, not just the GM and certainly including the player of the specific character, meets the PCs and gets to know who they are.
The question I have is how much do you allow tweaking in those first few sessions, provided you allow tweaking at all? Can people fully remake their character? Change a thing here or there? Does it matter if something the player wants to drop has already been a prominent feature of a game session or not?
How do you do it?
As a note, we will not have a post on Monday, November 11th. Enjoy celebrating Veteran's Day if you are in a position to do so.